Analytic System for Graphical Interactive B-Spline Model Selection

1. A non-transitory computer-readable medium having stored thereon computer-readable instructions that when executed by a computing device cause the computing device to: read a dataset that includes a plurality of observation vectors, wherein each observation vector of the plurality of observation vectors includes an explanatory variable value and a response variable value; define a first knot location and a last knot location; for each number of internal knots value of a set of internal knot values, define a knot location for each internal knot of the respective number of internal knots value; for each polynomial degree value of a set of polynomial degree values, fit a b-spline type model using the first knot location, the last knot location, and the defined knot locations and the respective polynomial degree value, wherein the b-spline type model is further fit to the explanatory variable value and the response variable value of each observation vector of the plurality of observation vectors to define coefficients that describe a response variable; compute a fit criterion value for the fit b-spline type model that quantifies a goodness of the fit; and store the computed fit criterion value, the first knot location, the last knot location, the defined knot locations, the respective polynomial degree value, the respective number of internal knots value, and the defined coefficients to the computer-readable medium; determine a best fit b-spline model based on the stored, computed fit criterion value of each fit b-spline type model; present a criterion fit graph on a display, wherein the criterion fit graph includes a number of internal knots line that indicates the number of internal knots value of the determined best fit b-spline model and a polynomial degree curve for each polynomial degree value of the set of polynomial degree values, wherein each polynomial degree curve shows the stored, computed fit criterion value as a function of the set of internal knot values; present a best fit b-spline model graph on the display next to the presented criterion fit graph, wherein the best fit b-spline model graph includes a knot location line at each of the knot locations defined for the number of internal knots value of the determined best fit b-spline model and a best fit model curve that is a plot of the response variable value computed as a function of the explanatory variable value using the defined coefficients of the determined best fit b-spline model; receive an indicator that the number of internal knots line is moved to a different number of internal knots value; redefine the knot location for each internal knot based on the different number of internal knots value; determine a second best fit b-spline model based on the stored, computed fit criterion value having the different number of internal knots value for the respective number of internal knots value; and update the presented best fit b-spline model graph to show the knot location line at each of the redefined knot locations and a second best fit model curve that is a second plot of the explanatory variable value computed as a function of the response variable value using the defined coefficients of the determined second best fit b-spline model.

2. The non-transitory computer-readable medium of claim 1 , wherein the fit criterion value is computed for the fit b-spline type model using a predefined fit criterion method.

3. The non-transitory computer-readable medium of claim 2 , wherein the fit criterion method is predefined as a user input through a user interface.

4. The non-transitory computer-readable medium of claim 3 , wherein the predefined fit criterion method is selected from the group consisting of a Bayesian information criterion method, an Akaike information criterion method, a generalized cross-validation information criterion method, a robust generalized cross-validation information criterion method, and a corrected Akaike information criterion method.

5. The non-transitory computer-readable medium of claim 1 , wherein the set of internal knot values is received as a user input through a user interface.

6. The non-transitory computer-readable medium of claim 1 , wherein the set of polynomial degree values is received as a user input through a user interface.

7. The non-transitory computer-readable medium of claim 1 , wherein the knot location for each internal knot of the respective number of internal knots value is defined as an evenly spaced quantile value between zero and one based on the respective number of internal knots value.

8. The non-transitory computer-readable medium of claim 7 , wherein the first knot location is at zero and the last knot location is at one.

9. The non-transitory computer-readable medium of claim 1 , wherein the knot location for each internal knot of the respective number of internal knots value is defined from evenly spaced values computed for the explanatory variable values based on the respective number of internal knots value.

10. The non-transitory computer-readable medium of claim 9 , wherein the first knot location is at a minimum value of the explanatory variable values and the last knot location is at a maximum value of the explanatory variable values.

11. The non-transitory computer-readable medium of claim 1 , wherein the explanatory variable value is a quantile value computed for each explanatory variable value, wherein the quantile value is computed for each explanatory variable value before defining the knot location for each internal knot of the respective number of internal knots value.

12. The non-transitory computer-readable medium of claim 1 , wherein the number of internal knots line is moved by sliding the number of internal knots line left or right along an x-axis of the presented criterion fit graph that is defined by the set of internal knot values.

13. The non-transitory computer-readable medium of claim 12 , wherein the indicator is received after the computer-readable instructions further cause the computing device to detect a selection of the number of internal knots line, a movement of the number of internal knots line, and a drop of the number of internal knots line at the different number of internal knots value on the x-axis.

14. The non-transitory computer-readable medium of claim 1 , wherein the best fit b-spline model graph further includes a scatterplot of the response variable value read from the dataset and the explanatory variable value.

15. The non-transitory computer-readable medium of claim 1 , wherein the computer-readable instructions further cause the computing device to store the defined coefficients of the second best fit b-spline model and the redefined knot locations of the second best fit b-spline model to the computer-readable medium.

16. The non-transitory computer-readable medium of claim 15 , wherein parameters of the second best fit b-spline model are stored when a store indicator is received.

17. The non-transitory computer-readable medium of claim 15 , wherein the computer-readable instructions further cause the computing device to: read a second explanatory variable value from a scoring dataset; compute a new response variable value using the stored, defined coefficients and the redefined knot locations of the second best fit b-spline model; and output the computed new response variable value.

18. The non-transitory computer-readable medium of claim 1 , wherein the computer-readable instructions further cause the computing device to: receive a second indicator that at least one knot location line is moved to a different knot location; determine the different knot location of the at least one knot location line; redefine a second knot location for each internal knot of the respective number of internal knots value including the determined different knot location; for each polynomial degree value of the set of polynomial degree values, refit the b-spline type model using the first knot location, the last knot location, and the redefined second knot locations and the respective polynomial degree value to define second coefficients that describe the response variable; compute a second fit criterion value for the refit b-spline type model; and store the computed second fit criterion value, the first knot location, the last knot location, the redefined second knot locations, the respective polynomial degree value, the respective number of internal knots value, and the defined second coefficients to the computer-readable medium; determine a third best fit b-spline model based on the stored, computed second fit criterion value of each refit b-spline type model; and update the presented best fit b-spline model graph to show the knot location line at each of the redefined second knot locations and a third best fit model curve that is a third plot of the explanatory variable value computed as a function of the response variable value using the defined second coefficients of the determined third best fit b-spline model.

19. The non-transitory computer-readable medium of claim 18 , wherein the computer-readable instructions further cause the computing device to update the presented criterion fit graph to show a second polynomial degree curve for each polynomial degree value of the set of polynomial degree values, wherein each polynomial degree curve shows the stored, computed second fit criterion value as a function of the set of internal knot values.

20. The non-transitory computer-readable medium of claim 18 , wherein the computer-readable instructions further cause the computing device to store the second coefficients of the determined third best fit b-spline model and the redefined second knot locations to the computer-readable medium.

21. The non-transitory computer-readable medium of claim 20 , wherein parameters of the third best fit b-spline model are stored when a store indicator is received.

22. The non-transitory computer-readable medium of claim 20 , wherein the computer-readable instructions further cause the computing device to: read a second explanatory variable value from a scoring dataset; compute a new response variable value using the stored, second coefficients of the determined third best fit b-spline model and the redefined second knot locations; and output the computed new response variable value.

23. A computing device comprising: a processor; and a non-transitory computer-readable medium operably coupled to the processor, the computer-readable medium having computer-readable instructions stored thereon that, when executed by the processor, cause the computing device to read a dataset that includes a plurality of observation vectors, wherein each observation vector of the plurality of observation vectors includes an explanatory variable value and a response variable value; define a first knot location and a last knot location; for each number of internal knots value of a set of internal knot values, define a knot location for each internal knot of the respective number of internal knots value; for each polynomial degree value of a set of polynomial degree values, fit a b-spline type model using the first knot location, the last knot location, and the defined knot locations and the respective polynomial degree value, wherein the b-spline type model is further fit to the explanatory variable value and the response variable value of each observation vector of the plurality of observation vectors to define coefficients that describe a response variable; compute a fit criterion value for the fit b-spline type model that quantifies a goodness of the fit; and store the computed fit criterion value, the first knot location, the last knot location, the defined knot locations, the respective polynomial degree value, the respective number of internal knots value, and the defined coefficients to the computer-readable medium; determine a best fit b-spline model based on the stored, computed fit criterion value of each fit b-spline type model; present a criterion fit graph on a display, wherein the criterion fit graph includes a number of internal knots line that indicates the number of internal knots value of the determined best fit b-spline model and a polynomial degree curve for each polynomial degree value of the set of polynomial degree values, wherein each polynomial degree curve shows the stored, computed fit criterion value as a function of the set of internal knot values; present a best fit b-spline model graph on the display next to the presented criterion fit graph, wherein the best fit b-spline model graph includes a knot location line at each of the knot locations defined for the number of internal knots value of the determined best fit b-spline model and a best fit model curve that is a plot of the response variable value computed as a function of the explanatory variable value using the defined coefficients of the determined best fit b-spline model; receive an indicator that the number of internal knots line is moved to a different number of internal knots value; redefine the knot location for each internal knot based on the different number of internal knots value; determine a second best fit b-spline model based on the stored, computed fit criterion value having the different number of internal knots value for the respective number of internal knots value; and update the presented best fit b-spline model graph to show the knot location line at each of the redefined knot locations and a second best fit model curve that is a second plot of the explanatory variable value computed as a function of the response variable value using the defined coefficients of the determined second best fit b-spline model.

24. A method of providing interactive b-spline model selection, the method comprising: reading, by a computing device, a dataset that includes a plurality of observation vectors, wherein each observation vector of the plurality of observation vectors includes an explanatory variable value and a response variable value; defining, by the computing device, a first knot location and a last knot location; for each number of internal knots value of a set of internal knot values, defining, by the computing device, a knot location for each internal knot of the respective number of internal knots value; for each polynomial degree value of a set of polynomial degree values, fitting, by the computing device, a b-spline type model using the first knot location, the last knot location, and the defined knot locations and the respective polynomial degree value, wherein the b-spline type model is further fit to the explanatory variable value and the response variable value of each observation vector of the plurality of observation vectors to define coefficients that describe a response variable; computing, by the computing device, a fit criterion value for the fit b-spline type model that quantifies a goodness of the fit; and storing, by the computing device, the computed fit criterion value, the first knot location, the last knot location, the defined knot locations, the respective polynomial degree value, the respective number of internal knots value, and the defined coefficients to the computer-readable medium; determining, by the computing device, a best fit b-spline model based on the stored, computed fit criterion value of each fit b-spline type model; presenting, by the computing device, a criterion fit graph on a display, wherein the criterion fit graph includes a number of internal knots line that indicates the number of internal knots value of the determined best fit b-spline model and a polynomial degree curve for each polynomial degree value of the set of polynomial degree values, wherein each polynomial degree curve shows the stored, computed fit criterion value as a function of the set of internal knot values; presenting, by the computing device, a best fit b-spline model graph on the display next to the presented criterion fit graph, wherein the best fit b-spline model graph includes a knot location line at each of the knot locations defined for the number of internal knots value of the determined best fit b-spline model and a best fit model curve that is a plot of the response variable value computed as a function of the explanatory variable value using the defined coefficients of the determined best fit b-spline model; receiving, by the computing device, an indicator that the number of internal knots line is moved to a different number of internal knots value; redefining, by the computing device, the knot location for each internal knot based on the different number of internal knots value; determining, by the computing device, a second best fit b-spline model based on the stored, computed fit criterion value having the different number of internal knots value for the respective number of internal knots value; and updating, by the computing device, the presented best fit b-spline model graph to show the knot location line at each of the redefined knot locations and a second best fit model curve that is a second plot of the explanatory variable value computed as a function of the response variable value using the defined coefficients of the determined second best fit b-spline model.

25. The method of claim 24 , wherein the knot location for each internal knot of the respective number of internal knots value is defined as an evenly spaced quantile value between zero and one based on the respective number of internal knots value.

26. The method of claim 24 , wherein the knot location for each internal knot of the respective number of internal knots value is defined from evenly spaced values computed for the explanatory variable values based on the respective number of internal knots value.

27. The method of claim 24 , further comprising: receive a second indicator that at least one knot location line is moved to a different knot location; determining, by the computing device, the different knot location of the at least one knot location line; redefining, by the computing device, a second knot location for each internal knot of the respective number of internal knots value including the determined different knot location; for each polynomial degree value of the set of polynomial degree values, refitting, by the computing device, the b-spline type model using the first knot location, the last knot location, and the redefined second knot locations and the respective polynomial degree value to define second coefficients that describe the response variable; computing, by the computing device, a second fit criterion value for the refit b-spline type model; and storing, by the computing device, the computed second fit criterion value, the first knot location, the last knot location, the redefined second knot locations, the respective polynomial degree value, the respective number of internal knots value, and the defined second coefficients to the computer-readable medium; determining, by the computing device, a third best fit b-spline model based on the stored, computed second fit criterion value of each refit b-spline type model; and updating, by the computing device, the presented best fit b-spline model graph to show the knot location line at each of the redefined second knot locations and a third best fit model curve that is a third plot of the explanatory variable value computed as a function of the response variable value using the defined second coefficients of the determined third best fit b-spline model.

28. The method of claim 27 , further comprising updating, by the computing device, the presented criterion fit graph to show a second polynomial degree curve for each polynomial degree value of the set of polynomial degree values, wherein each polynomial degree curve shows the stored, computed second fit criterion value as a function of the set of internal knot values.

29. The method of claim 27 , further comprising storing, by the computing device, the second coefficients of the determined third best fit b-spline model and the redefined second knot locations to the computer-readable medium.

30. The method of claim 29 , wherein parameters of the third best fit b-spline model are stored when a store indicator is received.